We try to do things like detect partial solutions that might indicate the players are close to a full solution, because the worst thing is to bypass a puzzle when the players are actively engaged with it and having fun. On the other hand, if we know there's more interesting gameplay to come, and the players are spending ages on a particular puzzle, we want them to progress. This is the part where some enthusiasts disagree with our approach - some of them would rather fail than be pushed through. Fortunately, the bulk of our players would rather be given increasingly easy hints until they "solve" things themselves.